The expected degree of minimal spanning forests
نویسندگان
چکیده
منابع مشابه
Minimal spanning forests
We study minimal spanning forests in infinite graphs, which are weak limits of minimal spanning trees from finite subgraphs corresponding to i.i.d. random labels on the edges. These limits can be taken with free or wired boundary conditions, and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that ar...
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In this paper, we investigate the polynomial integrand of an integral formula that yields the expected length of the minimal spanning tree of a graph whose edges are uniformly distributed over the interval [0, 1]. In particular, we derive a general formula for the coefficients of the polynomial and use it to express the first few coefficients in terms of the structure of the underlying graph; e...
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The a.s. connectivity of the Euclidean minimal spanning forest MSF(X) on a homogeneous Poisson point process X ⊂ R is an open problem for dimension d > 2. We introduce a descending family of graphs (Gn)n≥2 that can be seen as approximations to the MSF in the sense that MSF(X) = ⋂∞ n=2Gn(X). For n = 2 one recovers the relative neighborhood graph or, in other words, the β-skeleton with β = 2. We ...
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Let G be a graph and S be a set of non-negative integers. By an S-degree free spanning forest of G we mean a spanning forest of G with no vertex degree in S. In this paper we study the existence of {0, 2}-degree free spanning forests in graphs. We show that if G is a graph with minimum degree at least 4, then there exists an {0, 2}-degree free spanning forest. Moreover, we show that every 2-con...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2016
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-014-3160-x